In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a...In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a,β〈1-1/p,which indicates that the weighted Bemstein-Durrmeyer operators have some better approxi- mation properties than the usual Bernstein-Durrmeyer operators.展开更多
In this paper, the capability of neural networks and some approximation problens in system identification with neural networks are investigated. Some results are given: (i) For any function g ∈Llocp (R1) ∩S’ (R1) t...In this paper, the capability of neural networks and some approximation problens in system identification with neural networks are investigated. Some results are given: (i) For any function g ∈Llocp (R1) ∩S’ (R1) to be an Lp-Tauber-Wiener function, it is necessary and sufficient that g is not apolynomial; (ii) If g∈(Lp TW), then the set of is dense in Lp(K)’ (iii) It is proved that bycompositions of some functions of one variable, one can approximate continuous functional defined on compact Lp(K) and continuous operators from compact Lp1(K1) to LP2(K2). These results confirm the capability of neural networks in identifying dynamic systems.展开更多
L^p approximation problems in system identification with RBF neural networks are investigated. It is proved that by superpositions of some functions of one variable in L^ploc（R）, one can approximate continuous funct...L^p approximation problems in system identification with RBF neural networks are investigated. It is proved that by superpositions of some functions of one variable in L^ploc（R）, one can approximate continuous functionals defined on a compact subset of L^P（K） and continuous operators from a compact subset of L^p1 （K1） to a compact subset of L^p2 （K2）. These results show that if its activation function is in L^ploc（R） and is not an even polynomial, then this RBF neural networks can approximate the above systems with any accuracy.展开更多
文摘In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a,β〈1-1/p,which indicates that the weighted Bemstein-Durrmeyer operators have some better approxi- mation properties than the usual Bernstein-Durrmeyer operators.
基金Project supported by the Climbing Programme-National Key Project for Fundamental Research in China, Grant NSC 92092 and NSF 19371022
文摘In this paper, the capability of neural networks and some approximation problens in system identification with neural networks are investigated. Some results are given: (i) For any function g ∈Llocp (R1) ∩S’ (R1) to be an Lp-Tauber-Wiener function, it is necessary and sufficient that g is not apolynomial; (ii) If g∈(Lp TW), then the set of is dense in Lp(K)’ (iii) It is proved that bycompositions of some functions of one variable, one can approximate continuous functional defined on compact Lp(K) and continuous operators from compact Lp1(K1) to LP2(K2). These results confirm the capability of neural networks in identifying dynamic systems.
基金Foundation item： tile National Natural Science Foundation of China （No. 10471017）.
文摘L^p approximation problems in system identification with RBF neural networks are investigated. It is proved that by superpositions of some functions of one variable in L^ploc（R）, one can approximate continuous functionals defined on a compact subset of L^P（K） and continuous operators from a compact subset of L^p1 （K1） to a compact subset of L^p2 （K2）. These results show that if its activation function is in L^ploc（R） and is not an even polynomial, then this RBF neural networks can approximate the above systems with any accuracy.
